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Non-linear sigma model approach to quantum spin chains

Sumathi Rao
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Abstract

We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b) field theories to describe fluctuations about the classical ordered phases and c) numerical methods. We then discuss the $J_1$-$J_2$-$δ$ model in some detail and end with a few comments on open problems.

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Sumathi Rao. 2005-12-05. Non-linear sigma model approach to quantum spin chains. https://arxiv.org/abs/cond-mat/0512085

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